Edits/corrections to doc pages 2315-2589
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@ -14,12 +14,12 @@ Syntax
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.. code-block:: LAMMPS
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pair_coeff i j eps sigma
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pair_coeff i j eps sigma cutoff
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pair_coeff i j eps sigma wca
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pair_coeff i j eps sigma cutoff wca
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pair_coeff I J eps sigma
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pair_coeff I J eps sigma cutoff
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pair_coeff I J eps sigma wca
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pair_coeff I J eps sigma cutoff wca
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* i,j = a particle type
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* I, J = a particle type
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* eps = interaction strength, i.e. the depth of the potential minimum (energy units)
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* sigma = distance of the potential minimum from 0
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* cutoff = the cutoff distance for this pair type, if different from global (distance units)
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@ -28,7 +28,7 @@ Description
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Style *coul/diel* computes a Coulomb correction for implicit solvent
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ion interactions in which the dielectric permittivity is distance dependent.
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The dielectric permittivity epsilon_D(r) connects to limiting regimes:
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The dielectric permittivity :math:`\epsilon_D(r)` connects to limiting regimes:
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One limit is defined by a small dielectric permittivity (close to vacuum)
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at or close to contact separation between the ions. At larger separations
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the dielectric permittivity reaches a bulk value used in the regular Coulomb
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@ -45,7 +45,7 @@ where :math:`r_{me}` is the inflection point of :math:`\epsilon_D(r)` and :math:
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defining length scale. C is the same Coulomb conversion factor as in the
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pair_styles coul/cut, coul/long, and coul/debye. In this way the Coulomb
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interaction between ions is corrected at small distances r. The lower
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limit of epsilon_D(r->0)=5.2 due to dielectric saturation :ref:`(Stiles) <Stiles>`
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limit of :math:`\epsilon_D(r \to 0) = 5.2` due to dielectric saturation :ref:`(Stiles) <Stiles>`
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while the Coulomb interaction reaches its bulk limit by setting
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:math:`\epsilon_D(r \to \infty) = \epsilon`, the bulk value of the solvent which is 78
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for water at 298K.
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@ -43,7 +43,7 @@ Examples
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Description
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"""""""""""
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Styles *coul/slater* compute electrostatic interactions in mesoscopic models
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Styles *coul/slater/** compute electrostatic interactions in mesoscopic models
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which employ potentials without explicit excluded-volume interactions.
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The goal is to prevent artificial ionic pair formation by including a charge
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distribution in the Coulomb potential, following the formulation of
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@ -129,7 +129,7 @@ torques do not act symmetrically. These formulas are discussed in
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Also note, that in the code, all of these terms (except Elj) have a
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:math:`C/\epsilon` prefactor, the same as the Coulombic term in the
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LJ + Coulombic pair styles discussed :doc:`here <pair_lj>`. C is an
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energy-conversion constant and epsilon is the dielectric constant
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energy-conversion constant and :math:`\epsilon` is the dielectric constant
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which can be set by the :doc:`dielectric <dielectric>` command. The
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same is true of the equations that follow for other dipole pair
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styles.
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@ -118,7 +118,7 @@ atoms types via the :doc:`pair_coeff <pair_coeff>` command are:
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The cutoff coefficient is optional.
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The GPU-accelerated versions of these styles are implemented based on
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Styles with a *gpu* suffix are implemented based on
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the work of :ref:`(Afshar) <Afshar>` and :ref:`(Phillips) <Phillips>`.
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.. note::
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@ -122,14 +122,6 @@ distance. The recommended cutoff for this pair style should follow
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the minimum image criterion, i.e. half of the minimum unit cell
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length.
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Style *eff/long* (not yet available) computes the same interactions as
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style *eff/cut* except that an additional damping factor is applied so
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it can be used in conjunction with the
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:doc:`kspace_style <kspace_style>` command and its *ewald* or *pppm*
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option. The Coulombic cutoff specified for this style means that
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pairwise interactions within this distance are computed directly;
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interactions outside that distance are computed in reciprocal space.
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This potential is designed to be used with :doc:`atom_style electron <atom_style>` definitions, in order to handle the
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description of systems with interacting nuclei and explicit electrons.
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@ -145,11 +137,6 @@ For *eff/cut*, the cutoff coefficient is optional. If it is not used
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(as in some of the examples above), the default global value specified
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in the pair_style command is used.
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For *eff/long* (not yet available) no cutoff will be specified for an
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individual I,J type pair via the :doc:`pair_coeff <pair_coeff>` command.
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All type pairs use the same global cutoff specified in the pair_style
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command.
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----------
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The *limit/eradius* and *pressure/evirials* keywords are optional.
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@ -190,7 +177,7 @@ representations, after the "ecp" keyword.
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.. note::
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there are two different pressures that can be reported for eFF
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There are two different pressures that can be reported for eFF
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when defining this pair_style, one (default) that considers electrons
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do not contribute radial virial components (i.e. electrons treated as
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incompressible 'rigid' spheres) and one that does. The radial
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@ -33,7 +33,7 @@ none
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Related commands
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""""""""""""""""
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`pair_tersoff <pair tersoff>`
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:doc:`pair_tersoff <pair_tersoff>`
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Default
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"""""""
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@ -80,7 +80,7 @@ The two Hookean styles use this formula:
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F_{hk} = (k_n \delta \mathbf{n}_{ij} -
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m_{eff} \gamma_n\mathbf{ v}_n) -
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(k_t \mathbf{ \Delta s}_t +
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(k_t \boldsymbol{\Delta} \mathbf{s}_t +
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m_{eff} \gamma_t \mathbf{v}_t)
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The Hertzian style uses this formula:
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@ -91,7 +91,7 @@ The Hertzian style uses this formula:
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\sqrt{\delta} \sqrt{\frac{R_i R_j}{R_i + R_j}}
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\Big[ (k_n \delta \mathbf{n}_{ij} -
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m_{eff} \: \gamma_n \mathbf{ v}_n) -
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(k_t \mathbf{ \Delta s}_t +
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(k_t \boldsymbol{\Delta} \mathbf{s}_t +
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m_{eff} \: \gamma_t \mathbf{v}_t) \Big]
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In both equations the first parenthesized term is the normal force
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@ -114,7 +114,7 @@ The other quantities in the equations are as follows:
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* :math:`\gamma_n` = viscoelastic damping constant for normal contact
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* :math:`\gamma_t` = viscoelastic damping constant for tangential contact
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* :math:`m_{eff} = M_i M_j / (M_i + M_j) =` effective mass of 2 particles of mass M_i and M_j
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* :math:`\mathbf{\Delta s}_t =` tangential displacement vector between 2 particles which is truncated to satisfy a frictional yield criterion
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* :math:`\boldsymbol{\Delta} \mathbf{s}_t =` tangential displacement vector between 2 particles which is truncated to satisfy a frictional yield criterion
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* :math:`n_{ij} =` unit vector along the line connecting the centers of the 2 particles
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* :math:`V_n =` normal component of the relative velocity of the 2 particles
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* :math:`V_t =` tangential component of the relative velocity of the 2 particles
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@ -328,7 +328,7 @@ keyword also affects the tangential damping. The parameter
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literature use :math:`x_{\gamma,t} = 1` (:ref:`Marshall <Marshall2009>`,
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:ref:`Tsuji et al <Tsuji1992>`, :ref:`Silbert et al <Silbert2001>`). The relative
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tangential velocity at the point of contact is given by
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:math:`\mathbf{v}_{t, rel} = \mathbf{v}_{t} - (R_i\mathbf{\Omega}_i + R_j\mathbf{\Omega}_j) \times \mathbf{n}`, where :math:`\mathbf{v}_{t} = \mathbf{v}_r - \mathbf{v}_r\cdot\mathbf{n}\ \mathbf{n}`,
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:math:`\mathbf{v}_{t, rel} = \mathbf{v}_{t} - (R_i\boldsymbol{\Omega}_i + R_j\boldsymbol{\Omega}_j) \times \mathbf{n}`, where :math:`\mathbf{v}_{t} = \mathbf{v}_r - \mathbf{v}_r\cdot\mathbf{n}\ \mathbf{n}`,
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:math:`\mathbf{v}_r = \mathbf{v}_j - \mathbf{v}_i` .
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The direction of the applied force is :math:`\mathbf{t} = \mathbf{v_{t,rel}}/\|\mathbf{v_{t,rel}}\|` .
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@ -548,7 +548,7 @@ the tangential force:
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\mathbf{F}_{roll,0} = k_{roll} \mathbf{\xi}_{roll} - \gamma_{roll} \mathbf{v}_{roll}
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Here, :math:`\mathbf{v}_{roll} = -R(\mathbf{\Omega}_i - \mathbf{\Omega}_j) \times \mathbf{n}` is the relative rolling
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Here, :math:`\mathbf{v}_{roll} = -R(\boldsymbol{\Omega}_i - \boldsymbol{\Omega}_j) \times \mathbf{n}` is the relative rolling
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velocity, as given in :ref:`Wang et al <Wang2015>` and
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:ref:`Luding <Luding2008>`. This differs from the expressions given by :ref:`Kuhn and Bagi <Kuhn2004>` and used in :ref:`Marshall <Marshall2009>`; see :ref:`Wang et al <Wang2015>` for details. The rolling displacement is given by:
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@ -188,7 +188,7 @@ specified for this style means that pairwise interactions within this
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distance are computed directly; interactions outside that distance are
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computed in reciprocal space.
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Style *coul/wolf* adds a Coulombic pairwise interaction via the Wolf
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Style *lj/cut/coul/wolf* adds a Coulombic pairwise interaction via the Wolf
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summation method, described in :ref:`Wolf <Wolf3>`, given by:
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.. math::
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